Re: The set of necessary FISONs

On 22.02.2025 18:09, FromTheRafters wrote:

After serious thinking WM wrote :

On 22.02.2025 13:15, Richard Damon wrote:
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Peano's successors are not induction.
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Induction is the axiom that lets your prove that a set contains the set of Natural Numbers. It isn't a "construction" technique.

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Induction is the feature, proven or claimed, that an element exists in the set and with any element also its successor.

 No,

Can't you understand English?
"With any element also its successor."
This is proven by me: F(1) ∈ F und F(n) ∈ F ==> F(n+1) ∈ F describes the infinite inductive set F of FISONs which can be omitted because
|ℕ \ {1, 2, 3, ..., n}| = ℵo.
It is proven by Zermelo using his axiom of infinity: { } and with every a also {a}.
Regards, WM